Percolation transitions and wetting transitions in stochastic models

Brazilian Journal of Physics

Volumn 30, Issue 1, 2000, Pages 83-96

  Katori, Makoto ^a  

^a CHUO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034349236     PISSN: 01039733     EISSN: None     Source Type: Journal    
DOI: 10.1590/S0103-97332000000100008     Document Type: Review

References (42)

1. [1] J. Marro and R. Dickman, Noneguilibrium Phase Transitions in Lattice Models, (Cambridge University Press, Cambridge, 1999).
2. [2] E. Domany and W. Kinzel, Phys. Rev. Lett. 53, 311 (1984).
3. [3] T. Tsuchiya and M. Katori, J. Phys. Soc. Jpn. 67, 1655 (1998).
4. [4] M. E. Fisher, J. Stat. Phys. 34, 667 (1984).
5. [5] D. K. Arrowsmith, P. Mason and J. W. Essam, Physica A 177, 267 (1991).
6. [6] J. W. Essam and A. J. Guttmann, Phys. Rev. E 52, 5849 (1995).
7. [7] W. Kinzel, Z. Phys. B 58, 229 (1985).
8. [8] B. Chopard and M. Droz, Cellular Automata Modeling of Physical Systems, (Cambridge University Press, Cambridge, 1998).
9. [9] T. M. Liggett, Interacting Particle Systems (Springer, New York, 1985).
10. [10] R. Durrett, Lecture Notes on Particle Systems and Percolation (Wadsworth and Brooks/Cole, Pacific Grove, CA, 1988) Section 5b.
11. [11] N. Konno, Phase Transitions of Interacting Particle Systems (World Scientific, Singapore, 1994).
12. [12] T. M. Liggett, Stochastic Interacting Systems: Contact, Voter and Exclusion Processes, (Springer, New York, 1999).
13. [13] R. Durrett and D. Griffeath, Ann. Probab. 11, 1 (1983).
14. [14] M. Katori and N. Konno, J. Phys. A: Math. Gen. 26, 6597 (1993).
15. [15] I. Jensen and R. Dickman, Physica A 203, 175 (1994).
16. [16] T. E. Harris, Ann. Probab. 2, 969 (1974).
17. [17] T. M. Liggett, The periodic threshold contact process, in Random Walks, Brownian Motion and Interacting Particle Systems, edited R. Durrett and H. Kesten (Birkhäuser, Boston, 1991) pp. 339-358.
18. [18] R. C. Brower, M. A. Furman and M. Moshe, Phys. Lett. B 76, 213 (1978).
19. [19] P. Grassberger and A. de la Torre, Ann. Phys. 122, 373 (1979).
20. [20] J. L. Cardy and R. L. Sugar, J. Phys. A: Math. Gen. 13, L423 (1980).
21. [21] R. Dickman and M. A. Burschka, Phys. Lett. A 127, 132 (1988).
22. [22] R. M. Ziff, E. Gulari and Y. Barshad, Phys. Rev. Lett. 56, 2553 (1986).
23. [23] R. Dickman and T. Tomé, Phys. Rev. A 44, 4833 (1991).
24. [24] M. Katori, J. Phys. A: Math. Gen. 27, 3191 (1994).
25. [25] M. Katori and H. Tsukahara, J. Phys. A: Math. Gen. 28, 3935 (1995).
26. [26] T. M. Liggett, Ann. Appl. Probab. 5, 613 (1995).
27. [27] D. Dhar, J. Phys. A: Math. Gen. 15, 1849 (1982).
28. [28] I. Jensen and A. J. Guttmann, J. Phys. A: Math. Gen. 28, 4813 (1995).
29. [29] J. Cardy and F. Colaiori, Phys. Rev. Lett. 82, 2232 (1999).
30. [30] M. Katori, T. Tsuchiya, N. Inui and H. Kakuno, Annals of Combinatorics 3, 337 (1999).
31. [31] D. K. Arrowsmith and J. W. Essam, J. Math. Phys. 18, 235 (1977).
32. [32] J. W. Essam, Percolation and cluster size, in Phase Transitions and Critical Phenomena, vol.2, C. Domb and M. S. Green, eds., (Academic Press, London, 1972) pp.197-270.
33. [33] J. W. Essam, Rep. Prog. Phys. 43, 833 (1980).
34. [34] N. Konno, in preparation.
35. [35] F. M. Bhatti and J. W. Essam, J. Phys. A: Math. Gen. 17, L67 (1984).
36. [36] D. A. Huse, A. M. Szpilka and M. E. Fisher, Physica A 121, 363 (1983).
37. [37] N. Inui and M. Katori, J. Phys. A: Math. Gen. 29, 4347 (1996).
38. [38] A. J. Guttmann, A. L. Owczarek and X. G. Viennot, J. Phys. A: Math. Gen. 31, 8123 (1998).
39. [39] A. J. Guttmann and M. Vöge, Lattice paths: Vicious walkers and friendly walkers, submitted to J. Stat. Inference and Planning (1999).
40. [40] R. J. Baxter, Exactly Solved Models in Statistical Mechanics (Academic Press, London, 1982).
41. [41] P. W. Kasteleyn and C. M. Fortuin, J. Phys. Soc. Jpn. Suppl. 26, 11 (1969).
42. [42] C. M. Fortuin and P. W. Kasteleyn, Physica 57, 536 (1972).